A parameterization method for the design of IIR digital filters with prescribed stability margin

A major problem in the design of recursive digital filters is the stability. Although an unstable recursive filter obtained from a design algorithm can be stabilized by reciprocal substitution of the unstable factors of the filter without changing its amplitude response, this stabilization technique cannot be applied if phase response is a part of the design specifications. In this paper, we propose a new method for the design of recursive digital filters with prescribed stability margin by parameterizing all stable transfer functions and carrying out unconstrained optimization over this class of transfer functions. A parameterization technique based on modified bilinear transformation is described and closed-form formulas for the gradient of several typical objective functions are derived